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by Claire Voisin and Leila Schneps Trans.

Edition: 03Copyright: 2003

Publisher: Cambridge University Press

Published: 2003

International: No

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The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry.

Introduction.

Part I. The Topology of Algebraic Varieties:

1. The Lefschetz theorem on hyperplane sections

2. Lefschetz pencils

3. Monodromy

4. The Leray spectral sequence

Part II. Variations of Hodge Structure:

5. Transversality and applications

6. Hodge filtration of hypersurfaces

7. Normal functions and infinitesimal invariants

8. Nori's work

Part III. Algebraic Cycles:

9. Chow groups

10. Mumford' theorem and its generalizations

11. The Bloch conjecture and its generalizations

Bibliography

Index.

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Summary

The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry.

Table of Contents

Introduction.

Part I. The Topology of Algebraic Varieties:

1. The Lefschetz theorem on hyperplane sections

2. Lefschetz pencils

3. Monodromy

4. The Leray spectral sequence

Part II. Variations of Hodge Structure:

5. Transversality and applications

6. Hodge filtration of hypersurfaces

7. Normal functions and infinitesimal invariants

8. Nori's work

Part III. Algebraic Cycles:

9. Chow groups

10. Mumford' theorem and its generalizations

11. The Bloch conjecture and its generalizations

Bibliography

Index.

Publisher Info

Publisher: Cambridge University Press

Published: 2003

International: No

Published: 2003

International: No

Introduction.

Part I. The Topology of Algebraic Varieties:

1. The Lefschetz theorem on hyperplane sections

2. Lefschetz pencils

3. Monodromy

4. The Leray spectral sequence

Part II. Variations of Hodge Structure:

5. Transversality and applications

6. Hodge filtration of hypersurfaces

7. Normal functions and infinitesimal invariants

8. Nori's work

Part III. Algebraic Cycles:

9. Chow groups

10. Mumford' theorem and its generalizations

11. The Bloch conjecture and its generalizations

Bibliography

Index.